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November 21, 2006

Philosophy as Stance

Posted by David Corfield

Over at Ars Mathematica, John gave an explanation for the vituperative nature of the pro- vs anti- string theory discussions in the blogosphere:

The unpleasant nature of the whole extended argument can be seen as a collective cry of agony on the part of physicists trying and - so far - failing to find a theory that goes beyond the Standard Model and general relativity. Both string theorists and their opponents are secretly miserable over this failure.

To which I added:

I don’t have the book to hand, but the philosopher of science Bas van Fraassen has an interesting account of what happens as scientists become more desperate when nothing works. This is in ‘The Empirical Stance’, where he discusses Sartre’s Theory of the Emotions.

In Sketch for a Theory of the Emotions, Sartre replaces the traditional picture of the passivity of our emotional nature with one of the subject’s active participation in her emotional experiences. Emotion originates in a degradation of consciousness faced with a certain situation. The spontaneous conscious grasp of the situation which characterizes an emotion, involves what Sartre describes as a ‘magical’ transformation of the situation. Faced with an object which poses an insurmountable problem, the subject attempts to view it differently, as though it were magically transformed. Thus an imminent extreme danger may cause me to faint so that the object of my fear is no longer in my conscious grasp. Or, in the case of wrath against an unmovable obstacle, I may hit it as though the world were such that this action could lead to its removal. The essence of an emotional state is thus not an immanent feature of the mental world, but rather a transformation of the subject’s perspective upon the world.

Without an unmovable obstacle to hit, there are always other people.

Now, I do have The Empirical Stance (Yale, 2002) to hand, and have reread the relevant section (pp. 103-108) on the similar roles played by emotion for Sartre in our daily lives, and the distress caused by a research program failing to resolve its problems for the scientist. Van Fraassen is trying to make sense of the passage through a revolution from one theory to another which initially seemed nonsensical. He compares this with the process in Kafka’s Metamorphosis of the change from seeing a being as a family member to seeing it as a loathesome insect. Emotion, here, enables the cognitive transformation.

There’s much to admire in van Fraassen’s book. I particularly like his description of philosophy as based on the adoption of stances:

a philosophical position can consist in something other than a belief in what the world is like. We can, for example, take the empiricist’s attitude toward science rather than his or her beliefs about it as the more crucial characteristic…A philosophical position can consist in a stance (attitude, commitment, approach, a cluster of such - possibly including some propositional attitudes such as beliefs as well). Such a stance can of course be expressed, and may involve or presuppose some beliefs as well, but cannot be simply equated with having beliefs or making assertions about what there is. (pp. 47-48)

I am sympathetic to the stance of his opening chapter Against Analytic Metaphysics, and to his call for philosophy to change, to become

an engaged project in the world, self-conscious and conscious of what sort of enterprise it is. (p. 195)

But, as I outline here, my stance is more ‘historical’ than ‘empirical’.

That posts ends in MacIntyre’s endorsement of Collingwood’s ‘Historical Stance’. Like van Fraassen, MacIntyre makes the move of likening an everday crisis to one in the sciences, in his Epistemological Crises, Dramatic Narrative and the Philosophy of Science, a paper I discussed here. I see now all more clearly how crucial is one’s philosophy of history.

Posted at November 21, 2006 12:28 PM UTC

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Re: Philosophy as Stance

Thanks David and John. I particularly enjoy this n-category blog for its “spectral dimension”. Showing appreciation not just for a variety of fields for example appreciating besides physics also informatics as a true science, but on top of this doing so as well in a conceptual, a purely mathematical, a philosophical and even a socio-historical perspective. A bright sparkle of renaissance above the file cabinet of the sciences. :)

knapp daneben ist auch vorbei

cry of agony on the part of physicists trying and - so far - failing to find a theory that goes beyond the Standard Model and general relativity.

As I perceive it, the main heat in the controversy is caused by the fact that, while the search failed, it seemd to be so awfully close to its goal in many respects. Close and yet not right.

That’s, as far as I can tell, what turns participants in the discussion into “believers” and “non-believers”.

If the hypothesis of string theory had just plain failed to imply anything one was hoping for, it would have long been abandoned.

The crucial point seems to be that from the hypothesis of string theory follow lots of things that are of the right nature of what one is looking for - while still failing to be precisely what one is looking for.

This is what makes the situation so peculiar. 20 years of almost being there may be much harder to deal with than 20 years of having no good clue at all.

Most everything of the “string war” controversy that I have seen revolves around the question of how to evaluate the vastness of achievements that are undoubtly there in light of the fact that none of them so far yield exactly what we want.

Are these achievements a strong hint that one is on the right track? Or is the fact that the theory comes so close to its goal, while still not hitting it yet, just a trap that keeps us from acknowledging its failure?

And I think that’s a mighty question: string theory has been the study of a rather remarkable formal structure which does exist (in the world where mathematical concepts exist). Also, it gives rise to lots of qualitative features of the world around us. For one, it is like a huge encyclopedia of all kinds of gauge theories, with all sorts of interdependecies between them.

What would it mean if this huge structure in the space of theories is unrelated to reality?

Re: knapp daneben ist auch vorbei

it seemed to be so awfully close to its goal in many respects. Close and yet not right.

This puts me in mind of an experiment carried out by the psychologist Kurt Lewin, in, I think, the 1920s. I’ll probably mangle the details. The subject was told to stand inside a rectangle and with a few props contrive to reach an object placed outside in three different ways. Two ways could be found reasonably quickly, but there was no third way. Lewin noted the emotional breakdown of the subjects as their frustration mounted. I seem to recall that some even suffered hallucinations.

Re: knapp daneben ist auch vorbei

Right. So it all comes down to whether or not you feel you can trust the information that a third way exists.

And that’s what the fight in the “string wars” is over.

Some say: “there is every reason to expect that the third way to reach that object exists - because we already found two other ways and because a higher authority told us a third way does exist”.

The others say: “you have found two ways rather quickly, but have tried to find the third way for over 20 years. If you stopped trusting that higher authority and just pragmatically looked at your situation, you would realize that the existence of the third way must be an illusion.”

But neither of them can really know - unless (and until) the third way is actually found (which of course may never happen).

But compare this to the situation where the person in the square didn’t find even a single way to grab that object. In that case it would be much easier to abandon the whole idea and no controversy would ensue.

Re: knapp daneben ist auch vorbei

I find it interesting (in that Pynchonesque way) that Kurt Lewin is renowned for a social psychological concept known as field theory:

For Kurt Lewin behaviour was determined by totality of an individual’s situation. In his field theory, a ‘field’ is defined as ‘the totality of coexisting facts which are conceived of as mutually interdependent’ (Lewin 1951: 240). Individuals were seen to behave differently according to the way in which tensions between perceptions of the self and of the environment were worked through. The whole psychological field, or ‘lifespace’, within which people acted had to be viewed, in order to understand behaviour. Within this individuals and groups could be seen in topological terms (using map-like representations). Individuals participate in a series of life spaces (such as the family, work, school and church), and these were constructed under the influence of various force vectors (Lewin 1952).

This sounds perilously close to Lacanian topology, but I’m hardly qualified to judge.

Re: knapp daneben ist auch vorbei

Lewin’s topology seems more prosaic to me. Lacan’s topology concerned spaces of signifiers or the ‘dit-mensions’ of our being. There are some good ideas buried in Lacan’s work, but not in his mathematical excursions, as I argue in an article I wrote a while ago. As I say in footnote 11, something Lacan said about these ‘dit-mensions’ gave me an idea about the relationship between formalism and intuition for the first philosophy paper I had published. It became chapter 7 of my book. The same idea lurks behind my comment and the succeeding one at Jacques Distler’s blog.

Yuri Manin captures well and poetically the relationship between mathematical formalism and intuition (Lacan’s Symbolic and Imaginary?):

…the most fascinating thing about algebra and geometry is the way they struggle to help each other to emerge from the chaos of non-being, from those dark depths of subconscious where all roots of intellectual creativity reside. What one “sees” geometrically must be conveyed to others in words and symbols. If the resulting text can never be a perfect vehicle for the private and personal vision, the vision itself can never achieve maturity without being subject to the test of written speech. The latter is, after all, the basis of the social existence of mathematics.

A skillful use of the interpretative algebraic language possesses also a definite therapeutic quality. It allows one to fight the obsession which often accompanies contemplation of enigmatic Rorschach’s blots of one’s imagination.

When a significant new unit of meaning (technically, a mathematical definition or a mathematical fact) emerges from such a struggle, the mathematical community spends some time elaborating all conceivable implications of this discovery. (As an example, imagine the development of the idea of a continuous function, or a Riemannian metric, or a structure sheaf.) Interiorized, these implications prepare new firm ground for further flights of imagination, and more often than not reveal the limitations of the initial formalization of the geometric intuition. Gradually the discrepancy between the limited scope of this unit of meaning and our newly educated and enhanced geometric vision becomes glaring, and the cycle repeats itself.

If in physics knapp daneben ist auch vorbei, or a miss is as good as a mile, perhaps in less precise subjects misses may still stimulate interesting ideas.

Re: knapp daneben ist auch vorbei

Re: knapp daneben ist auch vorbei

There’s also a riddle people sometimes ask each other, saying that in English there are only three words ending in “gry”. Most people find “angry” and “hungry” and then start getting frustrated, and may eventually enlist other people.

Re: Philosophy as Stance

I am sorry to intrude with an off-topic comment. Please delete this if you think it is not appropriate.

Yesterday I started reading Bergson’s “Creative Evolution”, and in the first pages he writes:

”(…) the human intellect feels at home among inanimate objects, more especially among solids, where our action finds its fulcrum and our industry its tools; that our concepts have been formed on the model of solids; that our logic is, pre-eminently, the logic of solids; that, consequently, our intellect triumphs in geometry, wherein is revealed the kinship of logical thought with unorganized matter, and where the intellect has only to follow its natural movement, after the lightest possible contact with experience, in order to go from discovery to discovery, sure that experience is following behind it and will justify it invariably.”

The first thought that came to my mind was whether n-Categories could somewhat be viewed (philosophically speaking) as an attempt to free oneself from the idea that “our logic is, pre-eminently, the logic of solids”.

I would very much appreciate a discussion on Bergson’s view and n-Categories, if that makes any sense of course, perhaps it would be more appropriate to post it separately.

geometry

our intellect triumphs in geometry

I think what is meant is that the human mind, when reasoning about math, has two modes of operation: a “digital mode”, where we just manipulate strings of symbols like any computer could do in principle, and an “analog” mode, where we use a built-in geometry plug-in that allows us to “visualize” what these symbols mean.

The second mode is usually quicker by orders of magnitude. But the digital mode is more exact. (Same for analog and digital computers.)

Now, I think that categories mix both these modes to some extent. But in their very nature, higher categories are actually more a manifestation of the “geometric” mode, than of anything else. I think.

That’s the reason why much of category theory can equivalently be done in terms of topological spaces: by geometrically realizing the nerve of a category, that category is a topological space. Analogous statements hold for higher categories.

So “everything is geometry” here (or maybe topology, rather). Only that our internal geometry-plugin only works up to three dimensional geometry. (Some people are said to be able to upgrade to four-dimensional geometry.)

This has the consequence that in order to reason about higher categories, (at least from n=4n=4-categories on) one is thrown back to the “digital mode” and has to reason about all these nice structures in terms of awkward symbols again, for instance those describing simplicial sets.

Re: geometry

The second [(analog)] mode is usually quicker by orders of magnitude. But the digital mode is more exact. (Same for analog and digital computers.)

Ah, but I think that the real reason why digital computers have become so useful (once they became possible) is not so much their exactness (this digital computer that I’m using now —a moderately buggy web browser running Jacque’s possibly perfect scripts on a very buggy operating system— is not exact) but rather their flexility: digital computers can be programmed. And the same thing is true, I would argue, about the algebraic and formal side of mathematics!

Re: geometry

the same thing is true, I would argue, about the algebraic and formal side of mathematics!

Would you not want to make a distinction between the flexibility of a formal language such as second-order logic or set theory, on the one hand, and the algebra of n-categories, on the other? Isn’t it one of the charms of the latter than it doesn’t allow any old garbage to be written, and that it’s tailored to the ‘geometry’ of the setting?

Re: geometry

The second [(analog)] mode is usually quicker by orders of magnitude. But the digital mode is more exact. (Same for analog and digital computers.)

Ah, but I think that the real reason why digital computers have become so useful [is that they] can be programmed

I agree, that’ true. But it goes a little beyond my analogy with human reasoning about math. Or doesn’t it?

Well, to give a more concrete implementation of that analogy:

Say you have a cube, and you would like to compute how it looks like from various directions.

An analog computer for that fixed task would be: take a photograph of the cube.

Literally, the computation here is lightning quick. (Although, as usual for analog computers, reading out the computation result, i.e. developing the photography, takes more time.)

Alternatively, you can use some trigonometry, and digital implementations of trigonometric functions, and get a digital computer to calculate the picture of the cube as viewed from the given angle.

This takes “much” longer than illuminating a photographic plate. (Well, on modern computers it might not take that long…)

The analogy here is, I think, quite clear. When asked to draw a cube as viewed from a given perspective, most humans switch on their internal geometry module and know quickly how to draw the 2d image.

Alternatively, they could sit down and compute, by manipulating symbols on a piece of paper, the coordinates of the points they have to draw.

That will take most humans that I know considerably longer. (But it will also produce more exact results).

But this situation changes as we are asked to draw not the projection of a 3-dimensional cube onto a 2-dimensional space, but, say, the projection of a 10-dimensional cube onto a 5-dimensional space.

Most people will not be able to do that in the “analog” fashion. But it’s still possible using the slow “digital” method.

And I think it’s an issue.

For instance, I can use my internal geometry plugin to very quickly determine the precise details of a nonabelian 2-cocycle with values in a strict 2-group.

Digitally, this is messy. There are all kinds of index permutations to be taken care of and there is a twist that has to be inserted here and there.

But using higher categories, I can think of this cocycle as a tetrahedron labeled in a certain way. With this image in mind, I can do a (partial) “analog computation” of the cocycle equation that is much quicker.

So that’s very nice. The intrinsical geometric nature of higher categories allows me to use my ability to internally visualize otherwise rather opaque “digital” structures.

Unfortunately, though, the analog reasoning here fails as I move up the dimensional ladder.

If you asked me to write down an analogous 6-cocycle, coming from a 6-simplex colored in a suitable category, I would have to sit down, invent lots of symbols for dealing with simplicial sets, and then fill pages with symbol manipulations.

Re: geometry

That will take most humans that I know considerably longer. (But it will also produce more exact results).

This parenthetical comment, while true, is not so important. Generally, the analog results will be good enough.

Most people will not be able to do that in the “analog” fashion. But it’s still possible using the slow “digital” method.

That this is still possible is the important thing about the digital method. It is flexible; it is programmable. (I think that even its exactness, in situations where precision is important, can also be seen as an aspect of this.)

I think that your main point —that the intuition behind higher categories is geometric, even though they must still be handled with masses of symbols as the dimension increases— is right on target.

Re: Philosophy as Stance

I suppose already the shift to toposes other than Set is a move towards a logic of varying qualities. E.g, we may have a logic whose truth values are: true, false, and not yet true. Solids can have such truth values, e.g., leaves may be always green, always red, green at first but end up red.

But what about the logic of higher categories? I don’t know if John has written this up somewhere, but as is suggested by remarks towards the end of this paper, categorified predicate logic appears to be a form of modal logic. I suppose that in turn might be turned into a modal logic of varying qualities. But again this could be a logic relevant to solids - ‘It is possibly the case that there exists a leaf which is not yet red’. Or could the variation also affect the modality, ‘It is not yet necessarily the case that …’.

Re: Philosophy as Stance

Re: Philosophy as Stance

David writes:

In Sketch for a Theory of the Emotions, Sartre replaces the traditional picture of the passivity of our emotional nature with one of the subject’s active participation in her emotional experiences. Emotion originates in a degradation of consciousness faced with a certain situation. The spontaneous conscious grasp of the situation which characterizes an emotion, involves what Sartre describes as a ‘magical’ transformation of the situation. Faced with an object which poses an insurmountable problem, the subject attempts to view it differently, as though it were magically transformed.

I disagree with the idea that emotion is a “degradation” of consciousness. Emotion is a fundamental and vital part of grasping any situation. Emotion comes before rationality, and underlies it.

This is especially clear from the viewpoint of evolutionary biology. Emotion came before reason. When a deer sees a tiger, it gets scared - this is practically what it means for the deer to be seeing a tiger, instead of a striped pattern of leaves. It doesn’t see a tiger, think “oh, that’s a tiger”, realize this presents an insurmountable problem, and then get scared by “attempting to view the situation differently”.

And, we’re not that different from the deer. We have language, so we can reason verbally, but this ability is resting on a more robust layer of cognition, which relies heavily on emotion. A person with reason but without emotion would be cognitively crippled. Such a person would have trouble surviving.

Re: Philosophy as Stance

I disagree with the idea that emotion is a “degradation” of consciousness. Emotion is a fundamental and vital part of grasping any situation. Emotion comes before rationality, and underlies it.

Yes, Sartre’s does seem an extraordinary view. Van Fraassen comments that he finds it an implausible view for the most part, too. But if we restrict its scope to the emotions experienced during prolonged periods of frustration or of life crisis, when an enigma needs resolving, it starts to seem more reasonable.

What you say about the deer might be closer to the more immediate emotions of the scientist which correspond to the feeling that they’re onto something important, or on the right or wrong track.

Re: Philosophy as Stance

J-P Sartre said

emotion is a “degradation” of consciousness

This is reminiscent of the Stoics, whom I’ve been reading about recently. In fact, it’s reminiscent of a lot of Greek philosophy, where a lot of people seem to have seen a state of extreme emotional calm and imperturbability as an ideal.

I agree with David that this sort of thing is more likely to appeal to people under extreme emotional stress from crises in their lives, such as being hunted by death squads (Cicero), chronically ill and in political exile (Seneca) or under sentence of death (Boethius).

I trust that n-Categories are not that stressful, even when they seem frustratingly slow …

Re: Philosophy as Stance

In van Fraassen’s attack on regarding inference to the best explanation(ibe) as rational, he makes the charge that given the underdetermination of theory by evidence, any best explanation is very probably false. Advocates of IBE Psillos and Ladyman both point out that underdetermination will afflict constructive empiricism aswell. van Fraassen replies by saying that from the empiricist stance, the risk involved is motivated, given the aims of one with the empiricist stance.

But surely then the question is, do those with an empiricist stance believe their stance - with all the attitudes that involves - is justified? If so, then there is a belief, contrary to van Fraassen, that will characterise a philosophical position like empiricism. But if one needn’t be justified to hold a stance like empiricism, it isn’t clear why this is any better than just holding an unjustified belief.

Re: Philosophy as Stance

It certainly seems fair to ask of van Fraassen that he justify his adoption of the Empirical Stance. But how to do such a thing? It’s not that we should expect him to provide a stance-neutral justification of his stance. I can’t see that there could be such a neutral standpoint from which to arbitrate. Instead, van Fraassen has to tell us his version of the story of the Empirical Stance, its successes and temporary obstacles later overcome, its views of the course of other stances, and how it makes sense of their perceptions of their own weaknesses.

But then this is not to behave in accordance with the Empirical Stance itself in its positive attitude towards the natural sciences as the best means of gaining knowledge. On the other hand, it is to behave just as Alasdair MacIntyre says any member of a tradition of enquiry - including the natural sciences, but also history, philosophy, theology - ought to behave, as I outlined here (p. 14 onwards in particular).

In sum, I don’t see how the Empirical Stance has the resources to do more than attack the Metaphysical Stance. On the other hand, the Historical Stance, taken in a MacIntyrean way, does have the resources to describe the form of justification that alone is possible to justify philosophical stances.

“Why should I be rational?”; Re: Philosophy as Stance

Sorry that I can’t recall the reference, but a philosopher once said that the problem at the core of the Empirical Stance is the unaswerable question: “What experimental evidence is there that the Empirical Stance is useful?” which he said reduces to the simpler but still unanswerable question: “Why should I be rational?” This seems to be some kind of fixed-point of recursion issue.